Are you sure you are extraverted?
You say,
> I'm pretty extroverted (whatever the hell that means)
But then you also say
> The extra noise and distractions in an open-plan force me to use more willpower to focus and end up depleting my mental energy.
And that's pretty close to the definition of introversion.
You know introversion / extraversion is not about being shy vs outgoing. That is a very common misconception.
Introversion means that social interactions and situations lacking privacy cause you to become tired and experience mental energy drain.
You might love hanging out with friends and being around people, it just makes you tired. Extraverts on the other hand experience an energy boost from social situations, even if they don't prefer being in some specific social situation (e.g. an extravert may hate going to work, but still feel that "buzz of activity" just from being around everyone).
It's about how your cognitive fatigue is triggered: is your fatigue triggered by social situations, or is your fatigue lessened by those situations.
The effect you describe about the fatigue your open plan space causes for you makes me strongly suspect you're much closer to the introvert side of the spectrum than you believe.